ColPMan is a multi-player serious game through which a team of players can experientially learn how to collaboratively operate a virtual in-house supply chain. In this game, the problem of operating the whole chain is divided into sub-problems and each of them is addressed by a different player. While playing the game, the sub-problems distributed to the players can be linked to one another in a certain way through communication among them. This paper provides a framework for mathematically analyzing the effects of (the way the sub-problems are linked through) the communication. This also clarifies what the players should discuss and learn in the debriefing session.